Question

Evaluate (x-2y) ²
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Answer 1

Answer: (x+2y)(x-2y)

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Answer 2

Answer:

$\boxed{\sf {x}^{2} - 4xy + {y}^{2}}$

Step-by-step explanation:

$\sf Expand \: the \: following: \\ \sf \implies {(x - 2y)}^{2} \\ \\ \sf \implies (x - 2y)(x - 2y) \\ \\ \sf \implies x(x - 2y) - 2y(x - 2y) \\ \\ \sf \implies (x)(x) - (x)(2y) - (x)(2y) - (2y)( - 2y) \\ \\ \sf \implies {x}^{2} - 2xy - 2xy - ( - 4 {y}^{2} ) \\ \\ \sf \implies {x}^{2} - 4xy - ( - 4 {y}^{2} ) \\ \\ \sf \implies {x}^{2} - 4xy + {y}^{2}$

Additional information:

Algebraic Formulae:

$\sf {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2b \: \: \: \: \: or \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {(a - b)}^{2} + 4ab \\ \\ \sf {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab\: \: \: \: \: or \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {(a + b)}^{2} - 4ab \\ \\ \sf {a}^{2} - {b}^{2} = (a + b)(a - b) \\ \\ \sf {a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab \: \: \: \: \: or \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {(a - b)}^{2} + 2ab$